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Complexity theory is the theory of determining the necessary resources for the solution of algorithmic problems and, therefore, the limits of what is possible with the available resources. An understanding of these limits prevents the search for non-existing efficient algorithms. This textbook considers randomization as a key concept and emphasizes the interplay between theory and practice: New branches of complexity theory continue to arise in response to new algorithmic concepts, and its results - such as the theory of NP-completeness - have influenced the development of all areas of computer science. The topics selected have implications for concrete applications, and the significance of complexity theory for today's computer science is stressed throughout.

Algorithms. --- Algorithmes --- Algorithms --- Computer Science --- Mathematical Theory --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Constructive mathematics. --- EPUB-LIV-FT LIVINFOR SPRINGER-B --- Mathematics, Constructive --- Algorism --- Computer science. --- Computer programming. --- Coding theory. --- Computer logic. --- Mathematical logic. --- Computer Science. --- Programming Techniques. --- Algorithm Analysis and Problem Complexity. --- Coding and Information Theory. --- Logics and Meanings of Programs. --- Mathematical Logic and Formal Languages. --- Algebra --- Arithmetic --- Foundations --- Logic, Symbolic and mathematical --- Computer software. --- Logic design. --- Data compression (Telecommunication) --- Digital electronics --- Information theory --- Machine theory --- Signal theory (Telecommunication) --- Computer programming --- Design, Logic --- Design of logic systems --- Electronic circuit design --- Logic circuits --- Switching theory --- Software, Computer --- Computer systems --- Informatics --- Science --- Information theory. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Computer science logic --- Communication theory --- Communication --- Cybernetics --- Computers --- Electronic computer programming --- Electronic data processing --- Electronic digital computers --- Programming (Electronic computers) --- Coding theory --- Programming